A Generative Prediction-Correction Framework for Long-time Emulations of Spatially-Resolved Climate Extremes

Accurately quantifying the increased risks of extreme weather events in the coming decades and centuries requires generating large ensembles of climate realization across a wide range of emissions scenarios. The vast range of dynamically relevant scales in the Earth system renders this task computationally infeasible using conventional numerical simulation of the dynamical equations. We propose a prediction-correction framework for generating climate forecasts and quantifying the risk of extreme events over multi decade time scales. Our approach consists of two generative steps performed in series: a conditional Gaussian emulation, followed by a non-Gaussian machine learned (ML) debiasing correction. The emulator assumes a spatial basis of Principal Component Analysis (PCA) modes computed from reference data whose time dependence is decomposed into long-term seasonal variations and daily fluctuations -- the former parameterized by the global mean temperature and the latter modeled as a Gaussian stochastic process. The ML correction consists of a conditional score-based diffusion model which is trained on specific paired training trajectories, including a reference and an emulation nudged towards that reference. This approach allows the training to be robust to the chaotic divergence of any single data set and enables the learned map to generalize to unseen chaotic trajectories. The performance of our approach is evaluated on CMIP6 data. When trained on a single realization of one warming scenario, our model accurately predicts the statistics of extreme events in different scenarios, successfully extrapolating beyond the distribution of training data. These results demonstrate the potential of the proposed framework to provide an efficient and accurate prediction of the statistics of extreme events in the global climate system.